Project from view(Bound)
You can tab into edit mode, select one face where you don't want the image to be, then hit shift + G select co-planar, it will select all the faces with the same normal (the same orientation).
Then you can use the option of the threshold to allow faces with a pretty much similar orientation to be selected,
Then you can finally use the search bar to extend your selection if needed.
depending the orientation of the other faces of you mesh you will have some cleaning to do, but this method should make things easier and faster